Kourtney Kardashian and Travis Barker took full advantage of being in Sin City for the Grammys ... having a wedding ceremony in the middle of the night at a wedding chapel ... i.e., they're married!!!

Kourtney and Travis walked into One Love Wedding Chapel around 1:30 AM Monday ... only hours after he performed live at the Grammys. We're told the two didn't allow the venue to take any photos, bringing their own photographer and security instead.

Sources connected to the couple tell TMZ ... they had a marriage license and presented it to the chapel's owner, who was also a witness.

We're told it was important to them that an Elvis impersonator officiate the wedding ... so Elvis pronounced them man and wife.

Our sources say this will not be the only ceremony to mark the couple's commitment. We're told there will be "several' other celebrations, with lots of fanfare.

TMZ broke the story ... Travis popped the question back in October at a beachside hotel in Montecito, CA ... but the lovebirds had been mum on a wedding date. So, this could have been a spur-of-the-moment thing, or they were always planning to get married this weekend in Vegas.

Kourtney and Travis haven't been shy about their whirlwind romance ... with tons of PDA all over the globe ... including make-out sessions on the beach, at Disneyland, in front of the Eiffel Tower, on the Venice canals and in New York City ... just to name a few.

It's the first marriage for Kourtney, who never said "I do" to ex Scott Disick despite having 3 children together.

For Travis, this is his third marriage. He was with his first wife, Melissa Kennedy, for only 9 months before he filed for divorce back in 2002. Travis married Shanna Moakler a few years later in 2004, but he filed for divorce after nearly 2 years in 2006 and in 2008 their divorce was finalized.

Sounds like Travis finally found his special someone in Kourtney ... remember, he said "forever wasn't long enough" with her.

Mazel tov!!!